On the automaton determinization of sets of superworks

We introduce the concept of a determinising automaton which, for every superword taken from a given set fed into its input, beginning with some step, at any time $t$ yields the value of the input word at time $t+1$, that is, predicts the input superword. We find a criterion whether a given set of superwords is determinisable, that is, whether for the set there exists a determinising automaton. We give the best (in some sense) method to design a determinising automaton for an arbitrary determinisable set of superwords. For some determinisable sets we present optimal and asymptotically optimal determinising automata.